Encyclopedia of Financial Models, 3 Volume Set

Mean-Variance Model for Portfolio Selection

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

HARRY M. MARKOWITZ, PhD

Consultant

PETTER N. KOLM, PhD

Director of the Mathematics in Finance M.S. Program and Clinical Associate Professor, Courant Institute of Mathematical Sciences, New York University

FRANCIS GUPTA, PhD

Director, Index Research & Design, Dow Jones Indexes

Abstract: The theory of portfolio selection together with capital asset pricing theory provides the foundation and the building blocks for the management of portfolios. The goal of portfolio selection is the construction of portfolios that maximize expected returns consistent with individually acceptable levels of risk. Using both historical data and investor expectations of future returns, portfolio selection uses modeling techniques to quantify expected portfolio returns and acceptable levels of portfolio risk and provides methods to select an optimal portfolio.

The theory of portfolio selection presented in this entry, often referred to as mean-variance portfolio analysis or simply mean-variance analysis, is a normative theory. A normative theory is one that describes a standard or norm of behavior that investors should pursue in constructing a portfolio rather than a prediction concerning actual behavior.

Asset pricing theory goes on to formalize the relationship that should exist between asset returns and risk if investors behave in a hypothesized manner. In contrast to a normative ...